Finite Group Databasebeta

← #14680378

Subgroups — #14680378

Order 2816.

1502 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66943C211yesmaximal, characteristic
2C2×#10622589C211yesmaximal, characteristic
3C2×#10622545C211yesmaximal, characteristic
4#13066868C214yesmaximal
5#13066867C214yesmaximal
6#13066846C211yesmaximal, characteristic
7#13066845C211yesmaximal, characteristic
8#13066845C211yesmaximal, characteristic
9C11×C4⋊#95C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2212yes—
16C22×Dic11⋊C4C2212yes—
17C22×Dic11⋊C4C2212yes—
18C22×Dic11⋊C4C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C2×#66943—24no—
22C2×#66943—24no—
23C2×#66943C418yescomplemented
24C2×C11×#95C2214yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30#10622589—24no—
31#10622545—24no—
32C23×C4×C11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×Dic11C2312yes—
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2311yescharacteristic
40C23×Dic11C2311yescharacteristic
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4C2×C414yes—
47C2×C42×C11—22no—
48C2×C42×C11—22no—
49C2×C42×C11Q814yes—
50C2×C4⋊Dic11—22no—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11—24no—
53C2×C4⋊Dic11—24no—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11C2×C418yes—
58C2×C4⋊Dic11C2×C414yes—
59C2×Dic11⋊C4—24no—
60C2×Dic11⋊C4—24no—
61C2×Dic11⋊C4—24no—
62C2×Dic11⋊C4—24no—
63C2×Dic11⋊C4—44no—
64C2×Dic11⋊C4—44no—
65C2×Dic11⋊C4C2×C418yes—
66C2×C4×Dic11—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11C2×C414yes—
69C2×C4×Dic11D414yes—
70C2×C4×Dic11D414yes—
71C2×C4×Dic11Q814yes—
72#66943—232no—
73C11×#95—44no—
74C11⋊#95—24no—
75C11⋊#95—24no—
76C11⋊#95—44no—
77C11⋊#95—44no—
78C11⋊#95—44no—
79#14283—111nomaximal, Sylow
80C24×C11C2411yescharacteristic
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—24no—
87C22×C4×C11—22no—
88C22×C4×C11—24no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11C22×C414yes—
97C22×C4×C11C22×C412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×Q814yes—
101C22×C4×C11C2×Q812yes—
102C22×C4×C11C2×Q812yes—
103C22×C4×C11#4112yes—
104C22×C4×C11#4112yes—
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—24no—
116C22×Dic11—22no—
117C22×Dic11—24no—
118C22×Dic11—24no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—24no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11C22×C414yes—
125C22×Dic11C22×C412yes—
126C22×Dic11C22×C412yes—
127C22×Dic11C2×D412yes—
128C22×Dic11C2×D412yes—
129C22×Dic11C2×D412yes—
130C22×Dic11C2×D412yes—
131C22×Dic11C2×Q814yes—
132C11×C4⋊C4—28no—
133C11×C4⋊C4—44no—
134C42×C11—28no—
135C4⋊Dic11—216no—
136C4⋊Dic11—28no—
137C4⋊Dic11—44no—
138Dic11⋊C4—216no—
139Dic11⋊C4—48no—
140Dic11⋊C4—48no—
141C4×Dic11—28no—
142C4×Dic11C22⋊C4116yes—
143C22×#125—111no—
144C2×#384—111no—
145C2×#376—111no—
146#1441—114no—
147#1441—114no—
148C4⋊#95—111no—
149C4⋊#95—111no—
150C4⋊#95—111no—
151C4⋊#95D1111yescharacteristic
152C23×C11C23×C411yescharacteristic
153C23×C11C22×D411yescharacteristic
154C23×C11C22×D411yescharacteristic
155C23×C11C22×Q811yescharacteristic
156C23×C11C22×Q811yescharacteristic
157C23×C11C2×#4111yescharacteristic
158C23×C11C2×#4111yescharacteristic
159C23×C11H(5,𝔽2)12yes—
160C23×C11H(5,𝔽2)12yes—
161C23×C112−1+412yes—
162C23×C112−1+412yes—
163C2×C4×C11—24no—
164C2×C4×C11—28no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—44no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—44no—
179C2×C4×C11—44no—
180C2×C4×C11C2×C22⋊C414yes—
181C2×C4×C11C4×Q814yes—
182C2×C4×C11C4×Q814yes—
183C2×C4×C11C22⋊Q814yes—
184C2×C4×C11C22⋊Q814yes—
185C2×C4×C11#12414yes—
186C2×C4×C11C4⋊Q814yes—
187C2×Dic11—24no—
188C2×Dic11—24no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—28no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—44no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—44no—
211C2×Dic11—44no—
212C2×Dic11C2×C22⋊C414yes—
213C2×Dic11C2×C22⋊C414yes—
214C2×#125—118no—
215C2×#125—224no—
216C2×#125—224no—
217C22×C4⋊C4—112no—
218C22×C4⋊C4—111no—
219C22×C4⋊C4—112no—
220C22×C4⋊C4—111no—
221C22×C4⋊C4—112no—
222C22×C4⋊C4—112no—
223C22×C4⋊C4C2×D1111yescharacteristic
224C22×C4⋊C4C2×D1111yescharacteristic
225C22×C42—111no—
226C22×C42—111no—
227C22×C42C2×D1111yescharacteristic
228#384—224no—
229#376—224no—
230C2×#95—112no—
231C2×#95—112no—
232C2×#95—114no—
233C2×#95—114no—
234C2×#95—114no—
235C2×#95C2×D1114yes—
236C22×C11C22×C22⋊C411yescharacteristic
237C22×C11C2×C4×Q811yescharacteristic
238C22×C11C2×C4×Q811yescharacteristic
239C22×C11#52012yes—
240C22×C11#52012yes—
241C22×C11C2×C22⋊Q811yescharacteristic
242C22×C11C2×C22⋊Q811yescharacteristic
243C22×C11C2×#12411yescharacteristic
244C22×C11C2×C4⋊Q811yescharacteristic
245C22×C11#53511yescharacteristic
246C22×C11#53511yescharacteristic
247C22×C11#53611yescharacteristic
248C22×C11#53611yescharacteristic
249C22×C11#53712yes—
250C22×C11#53712yes—
251C22×C11#54012yes—
252C22×C11#54012yes—
253C22×C11#54112yes—
254C22×C11#54112yes—
255C22×C11#54412yes—
256C22×C11#54412yes—
257C22×C11#54412yes—
258C22×C11#54412yes—
259C4×C11—44no—
260C4×C11—44no—
261C4×C11—82no—
262C4×C11#39118yes—
263Dic11—24no—
264Dic11—24no—
265Dic11—44no—
266Dic11—44no—
267Dic11—82no—
268C23×C4—111no—
269C23×C4—111no—
270C23×C4—112no—
271C23×C4—112no—
272C23×C4—112no—
273C23×C4C22×D1112yes—
274C23×C4C22×D1112yes—
275C23×C4C22×D1112yes—
276C23×C4C22×D1111yescharacteristic
277#125—2232no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—118no—
284C2×C4⋊C4—118no—
285C2×C4⋊C4—114no—
286C2×C4⋊C4—224no—
287C2×C4⋊C4—224no—
288C2×C4⋊C4—224no—
289C2×C4⋊C4—224no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—224no—
293C2×C4⋊C4—224no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—444no—
298C2×C4⋊C4—444no—
299C2×C4⋊C4C4×D1114yes—
300C2×C42—22no—
301C2×C42—22no—
302C2×C42—114no—
303C2×C42—114no—
304C2×C42—114no—
305C2×C42—114no—
306C2×C42—222no—
307C2×C42—222no—
308C2×C42Dic2214yes—
309#95—44no—
310#95—224no—
311#95—224no—
312#95—444no—
313#95—444no—
314#95—444no—
315C2×C11C2×#39111yescharacteristic
316C2×C11#231111yescharacteristic
317C2×C11#231111yescharacteristic
318C2×C11#233012yes—
319C2×C11#233012yes—
320C2×C11#262912yes—
321C2×C11#262912yes—
322C2×C11#264111yescharacteristic
323C2×C11#264211yescharacteristic
324C2×C11#266011yescharacteristic
325C2×C11#266011yescharacteristic
326C24C23×D1111yescharacteristic
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—24no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—112no—
343C22×C4—112no—
344C22×C4—112no—
345C22×C4—112no—
346C22×C4—112no—
347C22×C4—112no—
348C22×C4—114no—
349C22×C4—114no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—224no—
361C22×C4—224no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—224no—
368C22×C4—224no—
369C22×C4C2×Dic2214yes—
370C22×C4C2×Dic2212yes—
371C22×C4C2×C4×D1114yes—
372C22×C4C2×C4×D1112yes—
373C22×C4#433912yes—
374C22×C4D4×D1112yes—
375C22×C4D4×D1112yes—
376C22×C4#434112yes—
377C22×C4Q8×D1112yes—
378C4⋊C4—28no—
379C4⋊C4—44no—
380C4⋊C4—2216no—
381C4⋊C4—2216no—
382C4⋊C4—228no—
383C4⋊C4—448no—
384C4⋊C4—448no—
385C4⋊C4—444no—
386C42—28no—
387C42—1116no—
388C42—228no—
389C11#1428311yescharacteristic, complemented, Sylow
390C23C22×Dic2211yescharacteristic
391C23C22×C4×D1111yescharacteristic
392C23C2×#433911yescharacteristic
393C23C2×D4×D1111yescharacteristic
394C23C2×D4×D1111yescharacteristic
395C23C2×#434111yescharacteristic
396C23#6703712yes—
397C23C2×Q8×D1111yescharacteristic
398C23#6704012yes—
399C23#6704212yes—
400C23#6704312yes—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—28no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—42no—
418C2×C4—114no—
419C2×C4—114no—
420C2×C4—222no—
421C2×C4—222no—
422C2×C4—224no—
423C2×C4—224no—
424C2×C4—224no—
425C2×C4—224no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—224no—
429C2×C4—224no—
430C2×C4—224no—
431C2×C4—228no—
432C2×C4—224no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—444no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—444no—
443C2×C4—444no—
444C2×C4—442no—
445C2×C4C4×Dic2214yes—
446C2×C4#6693114yes—
447C2×C4C22⋊C4×D1114yes—
448C2×C4#6693814yes—
449C2×C4#6694014yes—
450C2×C4#6694114yes—
451C2×C4#6694914yes—
452C22C2×C4×Dic2211yescharacteristic
453C22C2×#6693111yescharacteristic
454C22C2×C22⋊C4×D1111yescharacteristic
455C22C2×#6693811yescharacteristic
456C22C2×#6694011yescharacteristic
457C22C2×#6694111yescharacteristic
458C22#1062303112yes—
459C22C2×#6694911yescharacteristic
460C22#1062305012yes—
461C22#1062307712yes—
462C22#1062309312yes—
463C22#1062310512yes—
464C22#1062311412yes—
465C22#1062313912yes—
466C22#1062315012yes—
467C22#1062315612yes—
468C22#1062316012yes—
469C22#1062320511yescharacteristic
470C22#1062320611yescharacteristic
471C22#1062322012yes—
472C22#1062324611yescharacteristic
473C22#1062325511yescharacteristic
474C22#1062326012yes—
475C4—44no—
476C4—44no—
477C4—82no—
478C4—224no—
479C4—224no—
480C4—444no—
481C4—444no—
482C4—882no—
483C4#1062225918yes—
484C2C2×#1062225911yescharacteristic
485C2#1307120611yescharacteristic
486C2#1307120711yescharacteristic
487C2#1307135312yes—
488C2#1307135612yes—
489C2#1307445012yes—
490C2#1307445112yes—
491C2#1307456011yescharacteristic
492C2#1307456511yescharacteristic
493C2#1307473811yescharacteristic
494C2#1307474011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, prime radical, cosocleC24×C11C24
hypercenterC4⋊#95D11
hypocenterC11#14283
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
23. C2×#66943C4semidirect
389. C11#14283semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#669432
C2×#106225892
C2×#106225452
#130668682
#130668672
#130668462
#130668452
C11×C4⋊#952
#1428311